The New Sudoku Players' Forum

[Mauriès Robert]

Hi Robert.
Beautiful resolution of a very difficult scheme.
Paolo

Thank you, Paolo.
François C. (Assistant Sudoku) solved it in 30 sequences not exceeding a length of 13, so I did some unnecessary sequences.
Moreover, François C. set the TDP level of the puzzle at 5, which corresponds to the SER level I think.
Friendly

[denis_berthier]

Hi Robert,
That must have bee a hard work to do all this by hand.

As I said in my first post, as it is in T&E(1), this puzzle must have a solution with braids. In fact, whips of length ≤ 13 are enough.
Here, instead, I'll give a solution with g-whips of length ≤ 12.
What's to be noticed, typical of hard puzzles, is the long sequence of eliminations before a Single appears.

Hidden Text: Show

***********************************************************************************************
*** SudoRules 20.1.s based on CSP-Rules 2.1.s, config = gW+SFin
*** using CLIPS 6.32-r764
***********************************************************************************************
singles ==> r5c6 = 9, r2c7 = 1
215 candidates, 1308 csp-links and 1308 links. Density = 5.69%
whip[1]: r5n6{c9 .} ==> r4c8 ≠ 6
finned-x-wing-in-columns: n9{c7 c3}{r8 r3} ==> r3c2 ≠ 9, r3c1 ≠ 9
whip[1]: r3n9{c8 .} ==> r2c8 ≠ 9
178 g-candidates, 1149 csp-glinks and 663 non-csp glinks
g-whip[5]: b9n9{r9c8 r8c789} - c3n9{r8 r2} - c3n2{r2 r7} - r7c9{n2 n3} - r7c7{n3 .} ==> r9c8 ≠ 4
whip[6]: c8n8{r8 r9} - b9n9{r9c8 r8c7} - c3n9{r8 r2} - c3n2{r2 r7} - r9n2{c1 c9} - b9n5{r9c9 .} ==> r8c8 ≠ 4
whip[6]: c8n8{r8 r9} - b9n9{r9c8 r8c7} - c3n9{r8 r2} - c3n2{r2 r7} - r9n2{c1 c9} - b9n5{r9c9 .} ==> r8c8 ≠ 3
g-whip[8]: c8n8{r8 r9} - b9n9{r9c8 r8c789} - c3n9{r8 r2} - c3n2{r2 r7} - r7n8{c3 c1} - r7n7{c1 c6} - r7n6{c6 c4} - b8n3{r7c4 .} ==> r8c4 ≠ 8
whip[11]: r2n9{c1 c3} - c3n2{r2 r7} - r7n7{c3 c6} - r9n7{c6 c2} - b4n7{r6c2 r4c3} - r4n1{c3 c4} - r4n6{c4 c6} - r4n8{c6 c1} - r7n8{c1 c4} - c6n8{r9 r1} - r1c3{n8 .} ==> r2c1 ≠ 7
g-whip[8]: c2n9{r6 r789} - c3n9{r8 r2} - c1n9{r2 r6} - r6n7{c1 c8} - r2n7{c8 c6} - b8n7{r7c6 r9c5} - r9n1{c5 c4} - r4n1{c4 .} ==> r6c2 ≠ 1
g-whip[9]: r4n1{c3 c4} - r4n6{c4 c6} - r4n8{c6 c1} - b4n4{r4c1 r5c3} - b4n1{r5c3 r5c2} - r9n1{c2 c5} - b8n7{r9c5 r789c6} - r2n7{c6 c8} - b6n7{r4c8 .} ==> r4c3 ≠ 7
whip[5]: c3n7{r2 r7} - c3n2{r7 r2} - c3n9{r2 r8} - c2n9{r8 r6} - c2n7{r6 .} ==> r3c1 ≠ 7
whip[8]: r6n9{c2 c1} - r2n9{c1 c3} - c3n2{r2 r7} - c3n7{r7 r1} - c2n7{r1 r9} - b4n7{r6c2 r4c1} - c7n7{r4 r3} - c5n7{r3 .} ==> r6c2 ≠ 3
g-whip[8]: b4n3{r5c2 r6c1} - r6n9{c1 c2} - b4n7{r6c2 r4c1} - b4n8{r4c1 r456c3} - r1c3{n8 n7} - b7n7{r7c3 r9c2} - c5n7{r9 r3} - c7n7{r3 .} ==> r5c2 ≠ 1
whip[1]: c2n1{r9 .} ==> r8c3 ≠ 1
whip[7]: c8n8{r9 r8} - b9n9{r8c8 r8c7} - c8n9{r9 r3} - c8n6{r3 r5} - c8n4{r5 r4} - r5n4{c9 c3} - r8c3{n4 .} ==> r9c8 ≠ 5
g-whip[8]: b7n1{r8c2 r9c2} - c2n9{r9 r6} - c2n7{r6 r123} - c3n7{r1 r7} - c3n2{r7 r2} - c3n9{r2 r8} - b9n9{r8c7 r9c8} - c8n8{r9 .} ==> r8c2 ≠ 8
whip[10]: r3n9{c7 c8} - c8n6{r3 r5} - c8n4{r5 r4} - r4n7{c8 c1} - r6c2{n7 n9} - r9n9{c2 c1} - r2n9{c1 c3} - r2n7{c3 c6} - r7n7{c6 c3} - c3n2{r7 .} ==> r3c7 ≠ 7
whip[8]: r1c3{n8 n7} - c7n7{r1 r4} - r4c1{n7 n4} - r4c8{n4 n5} - r6c8{n5 n3} - b4n3{r6c1 r5c2} - r1c2{n3 n6} - r3c2{n6 .} ==> r3c1 ≠ 8
whip[10]: c8n6{r5 r3} - c9n6{r3 r5} - c9n1{r5 r6} - r6n3{c9 c1} - r6n9{c1 c2} - r6n7{c2 c8} - r2c8{n7 n5} - c9n5{r1 r9} - r9n2{c9 c1} - r3c1{n2 .} ==> r5c8 ≠ 3
whip[11]: c1n3{r3 r6} - r6n9{c1 c2} - b4n7{r6c2 r4c1} - b6n7{r4c7 r6c8} - r3n7{c8 c5} - r2n7{c6 c3} - r1c3{n7 n8} - b2n8{r1c5 r3c4} - r4n8{c4 c6} - c6n6{r4 r7} - r7n7{c6 .} ==> r3c2 ≠ 3
whip[9]: r1c3{n7 n8} - r3c2{n8 n6} - r1c2{n6 n3} - r3c1{n3 n2} - r9n2{c1 c9} - b6n2{r5c9 r5c7} - r5n3{c7 c9} - r3c9{n3 n4} - r7c9{n4 .} ==> r2c3 ≠ 7
whip[7]: b9n3{r8c7 r7c9} - r6n3{c9 c1} - c2n3{r5 r1} - c6n3{r1 r2} - r2n7{c6 c8} - r6n7{c8 c2} - r6n9{c2 .} ==> r5c7 ≠ 3
whip[12]: c1n8{r9 r4} - b5n8{r4c4 r5c5} - r3n8{c5 c4} - b1n8{r3c2 r1c3} - c3n7{r1 r7} - c3n2{r7 r2} - b2n2{r2c4 r3c5} - b2n4{r3c5 r1c5} - c5n7{r1 r9} - r9n1{c5 c4} - r8c5{n1 n5} - r9c6{n5 .} ==> r9c2 ≠ 8
whip[3]: c2n3{r1 r5} - c2n8{r5 r3} - r1c3{n8 .} ==> r1c2 ≠ 7
whip[6]: r2n7{c6 c8} - r3n7{c8 c2} - r1c3{n7 n8} - c2n8{r3 r5} - b4n3{r5c2 r6c1} - r6n7{c1 .} ==> r1c6 ≠ 7, r1c5 ≠ 7
whip[6]: r2n7{c8 c6} - r3n7{c5 c2} - r1c3{n7 n8} - c2n8{r3 r5} - b4n3{r5c2 r6c1} - r6n7{c1 .} ==> r4c8 ≠ 7
whip[7]: c7n7{r4 r1} - r1c3{n7 n8} - c2n8{r3 r5} - c2n3{r5 r1} - r1c6{n3 n5} - b3n5{r1c7 r2c8} - r4c8{n5 .} ==> r4c7 ≠ 4
g-whip[11]: c5n7{r9 r3} - r2n7{c6 c8} - r2n5{c8 c456} - r1c5{n5 n8} - b2n4{r1c5 r3c4} - b2n2{r3c4 r2c4} - c3n2{r2 r7} - b9n2{r7c7 r9c9} - r9n5{c9 c456} - c5n5{r8 r6} - r6n2{c5 .} ==> r9c5 ≠ 4
g-whip[10]: c8n8{r8 r9} - b9n9{r9c8 r8c789} - c3n9{r8 r2} - c3n2{r2 r7} - r7n8{c3 c1} - r7n7{c1 c6} - r9c6{n7 n5} - r9c5{n5 n1} - r5c5{n1 n2} - c7n2{r5 .} ==> r8c5 ≠ 8
g-whip[12]: c3n9{r8 r2} - c3n2{r2 r7} - c3n7{r7 r1} - b1n8{r1c3 r123c2} - r5c2{n8 n3} - r6c1{n3 n7} - b7n7{r7c1 r9c2} - c2n1{r9 r8} - r8n6{c2 c4} - r8n3{c4 c7} - r7c9{n3 n4} - r7c7{n4 .} ==> r8c1 ≠ 9
g-whip[12]: c3n2{r7 r2} - r2n9{c3 c1} - r6n9{c1 c2} - b4n7{r6c2 r456c1} - b7n7{r7c1 r9c2} - c5n7{r9 r3} - r3n2{c5 c4} - b2n4{r3c4 r1c5} - b2n8{r1c5 r1c6} - r9c6{n8 n5} - r8c5{n5 n1} - c2n1{r8 .} ==> r7c3 ≠ 8
whip[10]: r5c7{n2 n4} - r4c8{n4 n5} - r4c7{n5 n7} - r1n7{c7 c3} - r7c3{n7 n4} - r7c9{n4 n3} - b8n3{r7c4 r8c4} - r8n4{c4 c5} - b9n4{r8c7 r9c9} - r1n4{c9 .} ==> r7c7 ≠ 2
hidden-single-in-a-column ==> r5c7 = 2
whip[5]: r8n3{c4 c7} - r7c7{n3 n4} - r7c9{n4 n2} - b7n2{r7c1 r9c1} - r9n4{c1 .} ==> r8c4 ≠ 4
whip[8]: r8n3{c4 c7} - r7c7{n3 n4} - r7c9{n4 n2} - c3n2{r7 r2} - r2c4{n2 n5} - r1c6{n5 n8} - r1c3{n8 n7} - r7c3{n7 .} ==> r3c4 ≠ 3
whip[8]: r8n3{c4 c7} - r7c7{n3 n4} - r7c9{n4 n2} - c3n2{r7 r2} - c3n9{r2 r8} - r8c2{n9 n1} - r9c2{n1 n7} - r7c3{n7 .} ==> r8c4 ≠ 6
whip[1]: r8n6{c2 .} ==> r7c1 ≠ 6
whip[8]: r7c7{n4 n3} - r7c9{n3 n2} - b7n2{r7c1 r9c1} - b1n2{r2c1 r2c3} - c3n9{r2 r8} - b9n9{r8c7 r9c8} - c8n8{r9 r8} - b7n8{r8c1 .} ==> r7c1 ≠ 4
whip[9]: c8n3{r3 r6} - c9n3{r5 r7} - c6n3{r7 r2} - b2n7{r2c6 r3c5} - b3n7{r3c8 r2c8} - r2n5{c8 c4} - r1n5{c5 c9} - r6n5{c9 c5} - c5n2{r6 .} ==> r1c7 ≠ 3
g-whip[8]: c3n2{r7 r2} - c3n9{r2 r8} - c7n9{r8 r3} - c7n3{r3 r789} - r7c9{n3 n4} - c7n4{r7 r1} - r1n7{c7 c3} - r7c3{n7 .} ==> r7c1 ≠ 2
g-whip[5]: b7n6{r8c1 r8c2} - c2n1{r8 r9} - c2n9{r9 r6} - b4n7{r6c2 r456c1} - r7c1{n7 .} ==> r8c1 ≠ 8
whip[5]: r9c8{n9 n8} - r8n8{c8 c3} - r7c1{n8 n7} - b4n7{r4c1 r6c2} - r6n9{c2 .} ==> r9c1 ≠ 9
whip[8]: c7n9{r3 r8} - r9c8{n9 n8} - r8n8{c8 c3} - b7n9{r8c3 r9c2} - c2n1{r9 r8} - r8n6{c2 c1} - r8n4{c1 c5} - r1n4{c5 .} ==> r3c7 ≠ 4
whip[7]: r7n6{c4 c6} - r7n8{c6 c1} - r7n7{c1 c3} - r1n7{c3 c7} - c7n4{r1 r8} - b7n4{r8c1 r9c1} - b7n2{r9c1 .} ==> r7c4 ≠ 4
whip[6]: r7n4{c9 c3} - r5n4{c3 c8} - c8n6{r5 r3} - r3c9{n6 n3} - r3c1{n3 n2} - r9n2{c1 .} ==> r9c9 ≠ 4
whip[5]: r9n4{c4 c1} - b7n2{r9c1 r7c3} - r2c3{n2 n9} - r8c3{n9 n8} - c8n8{r8 .} ==> r9c4 ≠ 8
whip[9]: r4n1{c3 c4} - c4n6{r4 r7} - c6n6{r7 r4} - r4n8{c6 c1} - r7c1{n8 n7} - r7c3{n7 n2} - r9c1{n2 n4} - c4n4{r9 r3} - c4n8{r3 .} ==> r4c3 ≠ 4
whip[8]: r3n8{c5 c2} - r5n8{c2 c3} - b4n4{r5c3 r4c1} - r9n4{c1 c4} - b2n4{r3c4 r3c5} - c8n4{r3 r5} - c8n6{r5 r3} - r3n7{c8 .} ==> r1c5 ≠ 8
whip[5]: r9c9{n5 n2} - b7n2{r9c1 r7c3} - c3n7{r7 r1} - r1c7{n7 n4} - r1c5{n4 .} ==> r1c9 ≠ 5
whip[5]: r9n2{c1 c9} - c9n5{r9 r6} - r4c8{n5 n4} - r4c1{n4 n8} - r7c1{n8 .} ==> r9c1 ≠ 7
whip[5]: r9n2{c1 c9} - c9n5{r9 r6} - r4c8{n5 n4} - r4c1{n4 n7} - r4c7{n7 .} ==> r9c1 ≠ 8
biv-chain[3]: r9c1{n4 n2} - c3n2{r7 r2} - c3n9{r2 r8} ==> r8c3 ≠ 4
biv-chain[3]: r8c3{n9 n8} - c8n8{r8 r9} - r9n9{c8 c2} ==> r8c2 ≠ 9
biv-chain[4]: r1c5{n5 n4} - c4n4{r3 r9} - r9c1{n4 n2} - r9c9{n2 n5} ==> r9c5 ≠ 5
whip[3]: b3n5{r2c8 r1c7} - b6n5{r4c7 r6c9} - c5n5{r6 .} ==> r8c8 ≠ 5
naked-pairs-in-a-block: b9{r8c8 r9c8}{n8 n9} ==> r8c7 ≠ 9
hidden-single-in-a-column ==> r3c7 = 9
whip[1]: c7n3{r8 .} ==> r7c9 ≠ 3
whip[5]: r9n2{c1 c9} - b9n5{r9c9 r8c7} - b3n5{r1c7 r2c8} - r2c4{n5 n3} - r8n3{c4 .} ==> r2c1 ≠ 2
whip[5]: r1c5{n4 n5} - r1c7{n5 n7} - r4c7{n7 n5} - r8n5{c7 c4} - b5n5{r4c4 .} ==> r1c9 ≠ 4
whip[5]: b3n4{r3c9 r1c7} - b9n4{r7c7 r7c9} - r8n4{c7 c1} - r9c1{n4 n2} - c9n2{r9 .} ==> r3c5 ≠ 4
whip[6]: r9n4{c4 c1} - b7n2{r9c1 r7c3} - c9n2{r7 r9} - c9n5{r9 r6} - r6c4{n5 n2} - r2n2{c4 .} ==> r9c4 ≠ 1
naked-triplets-in-a-row: r9{c1 c4 c9}{n2 n4 n5} ==> r9c6 ≠ 5
whip[4]: c5n7{r3 r9} - c2n7{r9 r6} - c2n9{r6 r9} - r9n1{c2 .} ==> r3c8 ≠ 7
hidden-pairs-in-a-block: b3{r1c7 r2c8}{n5 n7} ==> r2c8 ≠ 3, r1c7 ≠ 4
singles ==> r1c5 = 4, r9c4 = 4, r9c1 = 2, r9c9 = 5, r2c3 = 2, r2c1 = 9, r6c2 = 9, r8c3 = 9, r8c8 = 8, r9c8 = 9, r7c1 = 8, r7c9 = 2
whip[1]: r2n3{c6 .} ==> r1c6 ≠ 3
hidden-pairs-in-a-row: r1{n3 n6}{c2 c9} ==> r1c2 ≠ 8
naked-pairs-in-a-block: b1{r1c2 r3c1}{n3 n6} ==> r3c2 ≠ 6
x-wing-in-rows: n3{r1 r5}{c2 c9} ==> r6c9 ≠ 3, r3c9 ≠ 3
naked-single ==> r6c9 = 1
naked-pairs-in-a-block: b5{r6c4 r6c5}{n2 n5} ==> r4c6 ≠ 5, r4c4 ≠ 5
stte

[Mauriès Robert]

Hi Robert,
That must have bee a hard work to do all this by hand.

Hi Denis,
Long yes, but not difficult in the sense that I found it fairly easy to find the right sequences leading to an elimination. But I didn't do the work of optimizing the eliminations, because by hand when you hold one ... you take it! So I transcribed all the steps, knowing that some of them are probably not useful.
A friend who practices TDP, and with whom I exchange a lot, solved the puzzle in 30 steps with tracks from the targets to be eliminated developed only with singles (max length 13).
Comparing his work to mine, I realize that almost half of my eliminations were not necessary to succeed, especially the longest ones. I am therefore thinking of optimizing my resolution to reduce it as much as possible. In the same way, I will try to give a shorter resolution using the OR condition. All this is a matter of time for me who follows busy elsewhere, but this way I will have done the whole puzzle with useful lessons for me.
Sincerely
Robert

[denis_berthier]

Out of curiosity, I generated random grids and then took out all clues not on mini-diagonals, thus:

Code: Select all

 7 . 3 2 . 8 4 . 1
 . 2 . . 6 . . 3 .
 4 . 1 7 . 3 2 . 8
 2 . 6 5 . 7 1 . 9
 . 7 . . 1 . . 2 .
 8 . 4 9 . 2 6 . 5
 3 . 2 1 . 4 9 . 6
 . 9 . . 2 . . 4 .
 6 . 5 3 . 9 7 . 2

[...]
I made two tests. The first was to measure how long it takes to generate a random grid. This turns out to be 28 microseconds. To delete 36 clues leaving 45 is trivial. But then I checked how many of the resulting puzzles have more than one solution and the answer was not, as Denis and I expected, close to 0, but 31%!

I tried a complementary experiment, using gsf's generator of minimal puzzles from a given pattern.
I first gave it the following "eleven"''s pattern : ...XXX..X...X....XXX......XXX...X.......X.......X...XXX......XXX....X...X..XXX... and it generated 100 puzzles in less than 10s.
Then I gave it your pattern: X.XX.XX.X.X..X..X.X.XX.XX.XX.XX.XX.X.X..X..X.X.XX.XX.XX.XX.XX.X.X..X..X.X.XX.XX.X and it has now been running for 40 mins without generating anything.

[DEFISE]

As I said in my first post, as it is in T&E(1), this puzzle must have a solution with braids. In fact, whips of length ≤ 13 are enough.
Here, instead, I'll give a solution with g-whips of length ≤ 12.
....
stte[/hidden]

Hello Denis Berthier,

I told you in another section that I had written a program to calculate the shortest whips (or braids).
For this puzzle (Extreme5) I found W=13, like you.
But by checking your resolution with g-whips, I realized that I did not respect the definition of a whip well, and after correction I found W=14.
Could you please give us your resolution with simple whips (so no g-whip), so that I can see where the problem is.
Thank you.

Sincerely.

[denis_berthier]

I told you in another section that I had written a program to calculate the shortest whips (or braids).
For this puzzle (Extreme5) I found W=13, like you.
But by checking your resolution with g-whips, I realized that I did not respect the definition of a whip well, and after correction I found W=14.
Could you please give us your resolution with simple whips (so no g-whip), so that I can see where the problem is.

I made a typo when I wrote W=13; it's 14.

Hidden Text: Show

***********************************************************************************************
*** SudoRules 20.1.s based on CSP-Rules 2.1.s, config = W+SFin
*** using CLIPS 6.32-r764
***********************************************************************************************
singles ==> r5c6 = 9, r2c7 = 1
215 candidates, 1308 csp-links and 1308 links. Density = 5.69%
whip[1]: r5n6{c9 .} ==> r4c8 ≠ 6
finned-x-wing-in-columns: n9{c7 c3}{r8 r3} ==> r3c2 ≠ 9, r3c1 ≠ 9
whip[1]: r3n9{c8 .} ==> r2c8 ≠ 9
whip[6]: c8n8{r9 r8} - b9n9{r8c8 r8c7} - c3n9{r8 r2} - c3n2{r2 r7} - r9n2{c1 c9} - b9n5{r9c9 .} ==> r9c8 ≠ 4
whip[6]: c8n8{r8 r9} - b9n9{r9c8 r8c7} - c3n9{r8 r2} - c3n2{r2 r7} - r9n2{c1 c9} - b9n5{r9c9 .} ==> r8c8 ≠ 4
whip[6]: c8n8{r8 r9} - b9n9{r9c8 r8c7} - c3n9{r8 r2} - c3n2{r2 r7} - r9n2{c1 c9} - b9n5{r9c9 .} ==> r8c8 ≠ 3
whip[11]: r2n9{c1 c3} - c3n2{r2 r7} - r7n7{c3 c6} - r9n7{c6 c2} - b4n7{r6c2 r4c3} - r4n1{c3 c4} - r4n6{c4 c6} - r4n8{c6 c1} - r7n8{c1 c4} - c6n8{r9 r1} - r1c3{n8 .} ==> r2c1 ≠ 7
whip[9]: r6n9{c2 c1} - r6n7{c1 c8} - r6n3{c8 c9} - c9n1{r6 r5} - c3n1{r5 r8} - c3n9{r8 r2} - r2n7{c3 c6} - b8n7{r7c6 r9c5} - c5n1{r9 .} ==> r6c2 ≠ 1
whip[12]: c8n8{r9 r8} - b9n9{r8c8 r8c7} - c8n9{r9 r3} - c8n6{r3 r5} - c8n4{r5 r4} - r5n4{c9 c3} - r8c3{n4 n1} - r8c2{n1 n6} - r1n6{c2 c9} - c9n5{r1 r6} - c9n1{r6 r5} - c2n1{r5 .} ==> r9c8 ≠ 5
whip[13]: r3n9{c7 c8} - r9c8{n9 n8} - r8c8{n8 n5} - r2c8{n5 n3} - r6c8{n3 n7} - r4c8{n7 n4} - r4c7{n4 n5} - b3n5{r1c7 r1c9} - r1n6{c9 c2} - c2n7{r1 r9} - c5n7{r9 r1} - r2c6{n7 n5} - r9c6{n5 .} ==> r3c7 ≠ 7
whip[8]: r1c3{n8 n7} - c7n7{r1 r4} - r4c1{n7 n4} - r4c8{n4 n5} - r6c8{n5 n3} - b4n3{r6c1 r5c2} - r1c2{n3 n6} - r3c2{n6 .} ==> r3c1 ≠ 8
whip[13]: r2n9{c3 c1} - b1n2{r2c1 r3c1} - c1n3{r3 r6} - r6n9{c1 c2} - r6n7{c2 c8} - r4n7{c8 c1} - r3n7{c1 c5} - b3n7{r3c8 r1c7} - r1c3{n7 n8} - b2n8{r1c5 r3c4} - r4n8{c4 c6} - c6n6{r4 r7} - r7n7{c6 .} ==> r2c3 ≠ 7
whip[7]: c1n3{r3 r6} - r6n9{c1 c2} - r6n7{c2 c8} - c7n7{r4 r1} - c2n7{r1 r9} - c5n7{r9 r3} - r2n7{c6 .} ==> r3c2 ≠ 3
whip[9]: r1c3{n7 n8} - r3c2{n8 n6} - r1c2{n6 n3} - b4n3{r5c2 r6c1} - r6n9{c1 c2} - r6n7{c2 c8} - b3n7{r2c8 r1c7} - c2n7{r1 r9} - c5n7{r9 .} ==> r3c1 ≠ 7
whip[10]: c7n2{r5 r7} - c3n2{r7 r2} - c3n9{r2 r8} - c2n9{r9 r6} - c2n3{r6 r1} - b4n3{r5c2 r6c1} - r6n7{c1 c8} - r2n7{c8 c6} - c6n3{r2 r7} - b9n3{r7c7 .} ==> r5c7 ≠ 3
whip[12]: c8n6{r5 r3} - r1n6{c9 c2} - c2n3{r1 r6} - r6n9{c2 c1} - r6n7{c1 c8} - r2c8{n7 n5} - r4c8{n5 n4} - r4c7{n4 n5} - b9n5{r8c7 r9c9} - r9n2{c9 c1} - r2c1{n2 n3} - r3c1{n3 .} ==> r5c8 ≠ 3
whip[14]: c9n1{r5 r6} - b5n1{r6c5 r4c4} - c3n1{r4 r8} - c3n9{r8 r2} - c3n2{r2 r7} - r9n2{c1 c9} - c9n5{r9 r1} - r1n6{c9 c2} - c2n3{r1 r6} - r6n9{c2 c1} - r6n7{c1 c8} - r2n7{c8 c6} - c5n7{r3 r9} - r9n1{c5 .} ==> r5c2 ≠ 1
whip[1]: c2n1{r9 .} ==> r8c3 ≠ 1
whip[4]: c3n1{r4 r5} - b4n4{r5c3 r4c1} - r4c7{n4 n5} - r4c8{n5 .} ==> r4c3 ≠ 7
whip[6]: r6n9{c2 c1} - r6n7{c1 c8} - c7n7{r4 r1} - c3n7{r1 r7} - c3n2{r7 r2} - r2n9{c3 .} ==> r6c2 ≠ 3
whip[6]: b1n8{r3c2 r1c3} - c3n7{r1 r7} - c3n2{r7 r2} - c3n9{r2 r8} - b9n9{r8c7 r9c8} - c8n8{r9 .} ==> r8c2 ≠ 8
whip[12]: c1n8{r9 r4} - b5n8{r4c4 r5c5} - r3n8{c5 c4} - b1n8{r3c2 r1c3} - c3n7{r1 r7} - c3n2{r7 r2} - b2n2{r2c4 r3c5} - b2n4{r3c5 r1c5} - c5n7{r1 r9} - r9c6{n7 n5} - r8c5{n5 n1} - c2n1{r8 .} ==> r9c2 ≠ 8
whip[3]: c2n3{r1 r5} - c2n8{r5 r3} - r1c3{n8 .} ==> r1c2 ≠ 7
whip[6]: r2n7{c6 c8} - r3n7{c8 c2} - r1c3{n7 n8} - c2n8{r3 r5} - b4n3{r5c2 r6c1} - r6n7{c1 .} ==> r1c5 ≠ 7
whip[6]: r2n7{c6 c8} - r3n7{c8 c2} - r1c3{n7 n8} - c2n8{r3 r5} - b4n3{r5c2 r6c1} - r6n7{c1 .} ==> r1c6 ≠ 7
whip[6]: r2n7{c8 c6} - r3n7{c5 c2} - r1c3{n7 n8} - c2n8{r3 r5} - b4n3{r5c2 r6c1} - r6n7{c1 .} ==> r4c8 ≠ 7
whip[7]: c7n7{r4 r1} - r1c3{n7 n8} - c2n8{r3 r5} - c2n3{r5 r1} - r1c6{n3 n5} - b3n5{r1c7 r2c8} - r4c8{n5 .} ==> r4c7 ≠ 4
whip[12]: c5n7{r9 r3} - b2n4{r3c5 r3c4} - r3n2{c4 c1} - r9n2{c1 c9} - b6n2{r5c9 r5c7} - r7n2{c7 c3} - r2c3{n2 n9} - r2c1{n9 n3} - r2c6{n3 n5} - r9n5{c6 c4} - b5n5{r4c4 r6c5} - c5n2{r6 .} ==> r9c5 ≠ 4
whip[13]: r3n8{c5 c2} - r5n8{c2 c3} - r1c3{n8 n7} - c7n7{r1 r4} - r4c1{n7 n4} - r4c8{n4 n5} - r6c8{n5 n3} - r2c8{n3 n7} - b2n7{r2c6 r3c5} - b2n4{r3c5 r3c4} - r3n2{c4 c1} - r9n2{c1 c9} - r9n4{c9 .} ==> r1c5 ≠ 8
whip[9]: r1n6{c9 c2} - c2n3{r1 r5} - c2n8{r5 r3} - b2n8{r3c5 r1c6} - r1n3{c6 c7} - b3n5{r1c7 r2c8} - r2n7{c8 c6} - c6n3{r2 r7} - b9n3{r7c7 .} ==> r1c9 ≠ 4
whip[12]: r1c5{n4 n5} - b3n5{r1c7 r2c8} - r4c8{n5 n4} - b3n4{r3c8 r1c7} - b3n7{r1c7 r3c8} - b6n7{r6c8 r4c7} - r4c1{n7 n8} - b5n8{r4c4 r5c5} - r3c5{n8 n2} - r2c4{n2 n3} - r8n3{c4 c7} - c7n5{r8 .} ==> r3c4 ≠ 4
whip[1]: c4n4{r9 .} ==> r8c5 ≠ 4
whip[10]: r9c8{n9 n8} - r8c8{n8 n5} - r4c8{n5 n4} - b4n4{r4c1 r5c3} - r8c3{n4 n8} - r8c5{n8 n1} - c2n1{r8 r9} - c2n9{r9 r6} - c2n7{r6 r3} - r1c3{n7 .} ==> r8c7 ≠ 9
hidden-single-in-a-column ==> r3c7 = 9
hidden-pairs-in-a-column: c8{n8 n9}{r8 r9} ==> r8c8 ≠ 5
whip[4]: r8n3{c4 c7} - b9n5{r8c7 r9c9} - r9n2{c9 c1} - r9n4{c1 .} ==> r8c4 ≠ 4
whip[3]: r9n2{c1 c9} - b9n5{r9c9 r8c7} - r8n4{c7 .} ==> r9c1 ≠ 4
biv-chain[6]: r8n3{c4 c7} - b9n5{r8c7 r9c9} - r9n2{c9 c1} - c3n2{r7 r2} - c3n9{r2 r8} - r8c8{n9 n8} ==> r8c4 ≠ 8
whip[6]: r9n4{c4 c9} - b9n5{r9c9 r8c7} - r8n3{c7 c4} - r2c4{n3 n2} - b1n2{r2c1 r3c1} - r9n2{c1 .} ==> r9c4 ≠ 5
whip[7]: r9n4{c4 c9} - r9n2{c9 c1} - b1n2{r2c1 r2c3} - c3n9{r2 r8} - r8c8{n9 n8} - r8c5{n8 n5} - b9n5{r8c7 .} ==> r9c4 ≠ 1
whip[7]: r8n3{c4 c7} - b9n5{r8c7 r9c9} - r9n2{c9 c1} - r3n2{c1 c5} - b2n8{r3c5 r1c6} - r9c6{n8 n7} - b2n7{r2c6 .} ==> r3c4 ≠ 3
whip[8]: r8c8{n8 n9} - c3n9{r8 r2} - c3n2{r2 r7} - c7n2{r7 r5} - r5c5{n2 n1} - b8n1{r9c5 r8c4} - r8n3{c4 c7} - r8n5{c7 .} ==> r8c5 ≠ 8
biv-chain[6]: c3n9{r8 r2} - c3n2{r2 r7} - r9n2{c1 c9} - b9n5{r9c9 r8c7} - r8c5{n5 n1} - c2n1{r8 r9} ==> r9c2 ≠ 9
whip[8]: c5n7{r3 r9} - c2n7{r9 r6} - c2n9{r6 r8} - r8c8{n9 n8} - r8c3{n8 n4} - b4n4{r4c3 r4c1} - c8n4{r4 r5} - c8n6{r5 .} ==> r3c8 ≠ 7
biv-chain[3]: r1n7{c7 c3} - r3n7{c2 c5} - b2n4{r3c5 r1c5} ==> r1c7 ≠ 4
hidden-single-in-a-row ==> r1c5 = 4
whip[3]: b3n7{r2c8 r1c7} - r4c7{n7 n5} - c8n5{r4 .} ==> r2c8 ≠ 3
whip[3]: r4c7{n5 n7} - c8n7{r6 r2} - c8n5{r2 .} ==> r6c9 ≠ 5
whip[5]: r3n7{c5 c2} - r1c3{n7 n8} - c2n8{r1 r5} - c5n8{r5 r9} - c5n7{r9 .} ==> r3c5 ≠ 2
whip[1]: c5n2{r6 .} ==> r6c4 ≠ 2
whip[5]: r9n2{c1 c9} - c9n5{r9 r1} - r2c8{n5 n7} - r1c7{n7 n3} - r3n3{c8 .} ==> r3c1 ≠ 2
singles ==> r3c4 = 2, r2c1 ≠ 3
whip[1]: r2n3{c6 .} ==> r1c6 ≠ 3
hidden-pairs-in-a-row: r3{n7 n8}{c2 c5} ==> r3c2 ≠ 6
naked-pairs-in-a-block: b1{r1c3 r3c2}{n7 n8} ==> r1c2 ≠ 8
x-wing-in-columns: n3{c1 c8}{r3 r6} ==> r6c9 ≠ 3, r3c9 ≠ 3
naked-triplets-in-a-row: r6{c4 c5 c9}{n1 n5 n2} ==> r6c8 ≠ 5
whip[1]: r6n5{c5 .} ==> r4c4 ≠ 5, r4c6 ≠ 5
biv-chain[3]: b2n8{r1c6 r3c5} - b2n7{r3c5 r2c6} - c6n3{r2 r7} ==> r7c6 ≠ 8
biv-chain[4]: b9n5{r9c9 r8c7} - r8n3{c7 c4} - r2c4{n3 n5} - r6n5{c4 c5} ==> r9c5 ≠ 5
biv-chain[3]: r6n2{c9 c5} - c5n5{r6 r8} - b9n5{r8c7 r9c9} ==> r9c9 ≠ 2
singles ==> r9c1 = 2, r2c1 = 9, r2c3 = 2, r8c3 = 9, r8c8 = 8, r9c8 = 9, r6c2 = 9
whip[1]: b4n7{r6c1 .} ==> r7c1 ≠ 7
whip[1]: b7n8{r7c3 .} ==> r7c4 ≠ 8
x-wing-in-columns: n7{c2 c5}{r3 r9} ==> r9c6 ≠ 7
naked-pairs-in-a-column: c6{r1 r9}{n5 n8} ==> r4c6 ≠ 8, r2c6 ≠ 5
naked-single ==> r4c6 = 6
hidden-pairs-in-a-row: r9{n1 n7}{c2 c5} ==> r9c5 ≠ 8
x-wing-in-columns: n8{c2 c5}{r3 r5} ==> r5c3 ≠ 8
x-wing-in-columns: n5{c6 c9}{r1 r9} ==> r1c7 ≠ 5
biv-chain[3]: b8n4{r7c4 r9c4} - c4n8{r9 r4} - c1n8{r4 r7} ==> r7c1 ≠ 4
biv-chain[3]: c1n4{r8 r4} - r4c8{n4 n5} - c7n5{r4 r8} ==> r8c7 ≠ 4
hidden-single-in-a-row ==> r8c1 = 4
naked-pairs-in-a-column: c3{r1 r7}{n7 n8} ==> r4c3 ≠ 8
hidden-pairs-in-a-column: c7{n2 n4}{r5 r7} ==> r7c7 ≠ 3
biv-chain[3]: r1c2{n3 n6} - r8n6{c2 c4} - r8n3{c4 c7} ==> r1c7 ≠ 3
stte

[DEFISE]

Denis Berthier said:
I made a typo when I wrote W=13; it's 14.

Ok Denis, I prefer that !
About braids, I found B-rating = 11.

[denis_berthier]

About braids, I found B-rating = 11.

Yes, B=11. It's a rare example with B ≠ W
Can you post your resolution path ?

[DEFISE]

About braids, I found B-rating = 11.

Yes, B=11. It's a rare example with B ≠ W
Can you post your resolution path ?

Yes of course but, sorry for my presentation of the braids :
-between the braces there are the target and only the right-linking candidates (no left-linking) :
{Target, R1, R2, … Rn-1}
-after the first symbol « => » there is the CSP variable which have no candidate compatible with the target and with the right-linking candidates.
-after the second symbol « => » it’s indicated that the target is deleted.
You can verify that the number of elements between the braces corresponds to the length of the braid.
For whose who do not understand french :
Candidat unique = single
Paire nue = nude pair
Paire cachée = hidden pair

Hidden Text: Show

Candidat unique: 1L2C7
Candidat unique: 9L5C6
Alignement: 6-L5-B6-L5C8-L5C9 => -6L4C8
1) {9L2C8,9L8C3,} => 9L9 vide => -9L2C8
Alignement: 9-L2-B1-L2C1-L2C3 => -9L3C1 -9L3C2
2) {3L8C8,8L9C8,9L8C7,9L2C3,2L7C3,4L7C7,} => L7C9 vide => -3L8C8
3) {4L8C8,8L9C8,9L8C7,9L2C3,2L7C3,3L7C7,} => L7C9 vide => -4L8C8
4) {4L9C8,8L8C8,9L8C7,9L2C3,2L7C3,3L7C7,} => L7C9 vide => -4L9C8
5) {8L8C4,3L8C7,8L9C8,9L8C8,9L2C3,2L7C3,4L7C7,} => L7C9 vide => -8L8C4
6) {7L2C1,8L1C3,9L2C3,2L7C3,7L7C6,7L4C3,1L4C4,6L4C6,8L4C1,8L7C4,} => 8C6 vide
=> -7L2C1
7) {1L6C2,1L4C4,9L6C1,9L2C3,7L6C8,7L2C6,1L9C5,} => 7C5 vide => -1L6C2
8) {7L4C3,1L4C4,6L4C6,8L4C1,7L6C8,7L2C6,7L9C5,1L9C2,1L5C3,} => 4B4 vide => -7L4C3
9) {7L3C1,7L7C3,7L6C2,9L6C1,9L2C3,} => 2C3 vide => -7L3C1
10) {3L6C2,9L6C1,9L2C3,7L6C8,7L2C6,7L4C1,7L7C3,} => 2C3 vide => -3L6C2
11) {7L3C7,9L3C8,9L8C7,9L2C3,7L2C6,2L7C3,7L7C1,7L4C8,4L5C8,} => 6C8 vide => -7L3C7
12) {1L5C2,3L6C1,9L6C2,7L4C1,7L1C7,8L1C3,} => 8B4 vide => -1L5C2
Alignement: 1-C2-B7-L8C2-L9C2 => -1L8C3
13) {5L9C8,8L8C8,9L3C8,9L8C7,4L8C3,4L4C1,4L5C8,} => 6C8 vide => -5L9C8
14) {8L3C1,7L1C3,7L4C7,4L4C1,5L4C8,3L6C8,3L5C2,6L1C2,} => L3C2 vide => -8L3C1
15) {8L8C2,8L4C1,1L9C2,8L9C8,9L9C1,4L8C3,} => 4C1 vide => -8L8C2
16) {3L5C7,3L6C1,9L6C2,7L6C8,3L8C4,2L7C7,2L2C3,7L2C6,3L2C8,3L3C2,} => 7L3 vide
=> -3L5C7
17) {3L5C8,6L5C9,6L1C2,3L6C1,2L3C1,9L2C1,7L2C3,5L2C8,2L9C9,1L6C9,} => 5C9 vide
=> -3L5C8
18) {9L8C1,9L2C3,9L6C2,2L7C3,7L1C3,7L9C2,1L8C2,6L8C4,3L8C7,4L7C7,} => L7C9 vide => -9L8C1
19) {3L3C2,8L5C2,3L6C1,9L6C2,7L6C8,7L3C5,7L2C3,8L3C4,7L4C1,8L4C6,7L7C6,}
=> 6C6 vide => -3L3C2
20) {7L2C3,8L1C3,6L3C2,3L1C2,3L5C9,4L3C9,2L7C9,} => 2C3 vide => -7L2C3
21) {7L1C5,8L1C3,7L7C3,2L2C3,7L4C7,7L6C1,3L5C2,8L5C5,8L3C4,2L3C5,} => 4B2 vide
=> -7L1C5
22) {4L9C5,4L3C4,7L3C5,7L2C8,2L3C1,2L2C4,5L2C6,2L9C9,2L6C5,5L9C4,} => 5C5 vide
=> -4L9C5
23) {2L6C9,4L5C7,2L9C1,4L3C8,4L1C5,1L5C9,8L5C3,7L1C3,4L7C3,3L7C9,3L8C4,}
=> 4L8 vide => -2L6C9
Alignement: 2-L6-B5-L6C4-L6C5 => -2L5C5
24) {9L9C1,8L9C8,9L2C3,9L6C2,2L7C3,7L1C3,7L9C2,5L9C6,1L9C5,8L5C5,4L8C5,}
=> L9C4 vide => -9L9C1
25) {8L8C1,8L9C8,9L9C2,7L6C2,4L8C3,1L8C2,5L8C5,7L9C6,7L7C1,} => 6B7 vide => -8L8C1
26) {8L8C5,1L5C5,8L9C8,9L9C2,4L8C3,1L9C4,4L9C9,2L9C1,2L2C3,} => 9C3 vide => -8L8C5
27) {4L3C7,4L1C5,9L3C8,8L9C8,5L8C8,1L8C5,1L9C2,} => 9L9 vide => -4L3C7
28) {4L4C7,7L1C7,8L1C3,5L8C7,4L3C8,4L1C5,1L8C5,8L5C5,1L9C2,} => 8C2 vide => -4L4C7
29) {5L8C8,8L8C3,8L4C1,8L5C5,8L9C8,9L9C2,1L8C2,4L8C5,5L1C5,} => 5L2 vide => -5L8C8
Paire nue: 89-C8-L8C8-L9C8 => -9L3C8
Candidat unique: 9L3C7
30) {4L8C4,3L8C7,5L9C9,2L9C1,} => 4L9 vide => -4L8C4
31) {3L3C4,3L8C7,3L7C6,6L4C6,5L9C9,2L9C1,2L3C5,5L2C4,} => 5C6 vide => -3L3C4
32) {7L4C8,5L4C7,3L6C8,7L2C6,7L3C2,8L1C3,3L5C2,8L9C2,5L9C6,} => 5L8 vide => -7L4C8
33) {7L9C2,1L8C2,7L3C5,9L8C3,2L2C3,2L3C4,4L1C5,5L8C5,8L9C6,} => 8B2 vide => -7L9C2
34) {4L7C3,2L2C3,9L2C1,9L6C2,7L1C3,} => 7C2 vide => -4L7C3
35) {8L7C3,7L1C3,7L6C2,9L6C1,9L2C3,} => 2C3 vide => -8L7C3
36) {8L5C3,7L1C3,1L5C5,2L7C3,9L2C3,4L8C3,5L8C5,2L9C9,} => 5L9 vide => -8L5C3
37) {8L1C5,8L3C2,} => 8L5 vide => -8L1C5
38) {8L9C5,8L5C2,3L1C2,7L3C5,7L1C3,} => 8B1 vide => -8L9C5
39) {8L4C6,1L5C5,4L5C3,7L4C1,5L4C7,5L9C9,7L9C5,} => L9C6 vide => -8L4C6
40) {8L9C4,8L7C1,8L4C3,7L1C3,7L9C1,2L9C9,} => 4L9 vide => -8L9C4
41) {4L9C9,2L9C1,2L2C3,5L8C7,3L8C4,5L2C4,4L1C5,1L8C5,} => L9C4 vide => -4L9C9
42) {4L7C4,4L9C1,4L8C7,2L9C9,} => 5B9 vide => -4L7C4
43) {5L9C4,5L8C7,3L8C4,4L8C5,5L1C5,5L2C8,7L2C6,7L9C5,} => 1B8 vide => -5L9C4
44) {4L3C4,5L1C5,1L9C4,4L9C1,2L9C9,5L6C9,2L6C4,3L2C4,3L8C7,} => 5C7 vide => -4L3C4
Candidat unique: 4L9C4
45) {9L9C2,1L9C5,5L8C5,5L9C9,2L9C1,2L2C3,} => 9C3 vide => -9L9C2
Candidat unique: 9L9C8
Candidat unique: 8L8C8
46) {1L6C5,8L5C5,1L4C3,8L4C1,1L9C2,} => 8B7 vide => -1L6C5
47) {6L4C4,1L4C3,8L4C1,8L1C3,8L9C2,6L7C6,} => 8C6 vide => -6L4C4
Candidat unique: 6L4C6
48) {8L1C6,7L1C3,8L3C2,8L9C1,8L7C4,6L7C1,} => 7B7 vide => -8L1C6
Alignement: 8-L1-B1-L1C2-L1C3 => -8L3C2
Alignement: 8-C6-B8-L7C6-L9C6 => -8L7C4
49) {6L1C2,7L3C2,9L6C2,1L8C2,1L9C5,} => 7C5 vide => -6L1C2
Candidat unique: 6L1C9
Candidat unique: 6L5C8
50) {5L2C4,5L1C7,5L8C5,} => 5C6 vide => -5L2C4
Paire cachee: 57-L2-L2C6-L2C8 => -3L2C6 -3L2C8
51) {3L1C7,3L8C4,} => 3C6 vide => -3L1C7
Alignement: 3-C7-B9-L7C7-L8C7 => -3L7C9
Alignement: 3-B3-L3-L3C8-L3C9 => -3L3C1
Paire cachee: 39-C1-L2C1-L6C1 => -2L2C1 -7L6C1
52) {7L1C2,7L6C8,} => 7C7 vide => -7L1C2
Paire nue: 38-C2-L1C2-L5C2 => -8L9C2
Candidat unique: 1L9C2
Alignement: 8-B7-C1-L7C1-L9C1 => -8L4C1
Paire cachee: 18-L4-L4C3-L4C4 => -4L4C3 -5L4C4
Alignement: 5-L4-B6-L4C7-L4C8 => -5L6C8 -5L6C9
Candidats uniques jusqu’à la fin.

Braids length <= 11
Run time = 321 s

[denis_berthier]

Hi Defise,
To me, this sequence of tracks looks more like the skeleton of a T&E solution, like any TDP solution. However, I see you have added a notion of length to that of a track, which makes it infinitely more interesting. But I guess Robert would say TDP is open, meaning it can take tidbits from everywhere.
While this is not a braids solution strictly speaking, it could probably be mapped to one by adding the proper information (CSP-Variables and left-linking candidates): at the time a track is used to make an elimination, are all the left and right linking candidates still present on the grid?

-between the braces there are the target and only the right-linking candidates (no left-linking) :
{Target, R1, R2, … Rn-1}
-after the first symbol « => » there is the CSP variable which have no candidate compatible with the target and with the right-linking candidates.
-after the second symbol « => » it’s indicated that the target is deleted.
You can verify that the number of elements between the braces corresponds to the length of the braid.

In the braces, you add the target (which is not a CSP-Var) and you miss the last CSP-Var, but +1-1 = 0 and the total is ok.
This notation misses the essence of a chain, i.e. the sequence of its CSP-Variables, as is made clear by treating the last one differently.

I should have asked you about your whips solution. In this notation, how can one check that a whip is different from a braid (i.e. the continuity condition llc-rlc-llc-....)? And especially, how do you do when you have both whips and braids in a resolution path?

[DEFISE]

Hello Denis,

Of course the candidates that I put between the braces are some candidates of a track (TDP) from the target. I think that concepts are one thing and how to program them is another. Simply, I don’t keep left-linking candidates to simplify computer programming and to save memory. Sorry but I finished my program a few days ago, maybe better later.

With my graphic tools I can easily restore left-linking candidates afterwards. That’s how I discovered my error (W=14 instead of W=13) because I saw that a whip was not one (it was a braid !).

[denis_berthier]

Of course the candidates that I put between the braces are some candidates of a track (TDP) from the target. I think that concepts are one thing and how to program them is another. Simply, I don’t keep left-linking candidates to simplify computer programming and to save memory.

I don't think keeping the llcs AND the CSP-Variables in addition to the rlcs would increase much memory requirements. That way you would have a real whips/braids solution and you could present them in a complete form.

With my graphic tools I can easily restore left-linking candidates afterwards.

I have no doubts about this and also about restoring the CSP-Variables, but the reader of your resolution paths doesn't have your graphic tools.

Now that you have added the notion of length to Robert's tracks, these appear for what they finally are: a degraded version of whips/braids.

[DEFISE]

Hello Denis,

Don’t worry, I do not intend to give my resolutions on this site with your method.
I just did it there because you asked me to. In fact what interests me is the result, ie the W-rating, because it was the subject of a serious statistical study on your part.
It's a very interesting idea I think, that's why I got interested in your work.

[denis_berthier]

Hello Denis,
Don’t worry, I do not intend to give my resolutions on this site with your method.
I just did it there because you asked me to. In fact what interests me is the result, ie the W-rating, because it was the subject of a serious statistical study on your part.
It's a very interesting idea I think, that's why I got interested in your work.

Hi defise
What should I worry about?
I don't mind at all if you give as many resolution paths as you want. This forum is open.
And I thank you for giving one that makes the relation of TDP with braids/whips totally clear for the first time.

There's something interesting in your remark about the rating. It's true that you can compute the rating without keeping track of the full whips/braids. As my main interest was the full resolution path, I've never tried to implement a reduced version of whips/braids that I could use only for rating purposes; so, I'm not sure how much gain in speed or memory it'd allow within my programming techniques (relying on an independent inference engine). I'll keep this idea in mind in case I have some free time to experiment with it.

[DEFISE]

Hello Denis,
I wonder about braids and whips.
In your PCS document (Nov 2012) you said p108, in the definition of braid :
« for any 1< k ≤ n, Lk is linked either to a previous right-linking candidate (some Ri, i < k) or to the target; this is the only (but major) structural difference with whips (for which the only linking possibility is Rk-1) »

I deduce that in a whip Lk must not be linked to the target nor to a Ri , i < k-1.
Is this right ?